Throughout the biological world, simple interactions between molecules, cells, or organisms lead to complex emergent dynamics that manifest in gene regulation, human disease, and population dynamics, all of which are in turn intertwined. Understanding biology therefore requires that we understand not only each interaction individually, but also how the system as a whole behaves; this is the premise of systems biology. Complex network structure can lead to a wide array of emergent behavior from simple building blocks, and understanding how this happens has the potential to improve our ability to understand and manipulate systems across biology, thus leading to advances in healthcare, biotechnology, and environmental science. The recent explosive growth in data collection tools has lead to a corresponding explosion in heuristic statistical solutions to biological questions. While these methods provide answers ad-hoc, the scientific community requires a more rigorous and holistic view in order to advance beyond a superficial understanding of biological systems, as is apparent in the inclusion of a call to understand the "rules of life" in the National Science Foundation's \emph{10 Big Ideas}. Within the broader scientific community there has been an emerging awareness of the power of mathematics to provide a systematic and thorough understanding of biological phenomena; mathematics provides the tools for discovering and describing the rules of life. A mathematical and systems biology approach provides an understanding that can be adapted to novel situations and perturbations of biological process. For example, a foundational understanding of the network of interactions between microbes in the human gut is necessary to design personalized treatments for dysbiosis and opportunistic infections.

The Microbiome

The human body contains a complex living ecosystem of microbial life known as the "human microbiome". This ecosystem and the metabolic activity of its member species has a profound impact on human health and disease. While this impact is clear in data, prediction of how the microbiome will effect host health and how host activity will effect the microbiome is currently difficult and limited to conclusions drawn from statistical association. In my work, I combine metabolic modeling with population dynamics to understand the human microbiome on a mechanistic level.

Epigenetics and Gene Regulation

The regulation of gene expression is managed through a variety of methods including epigenetic processes (e.g., DNA methylation). Understanding the role of epigenetic changes in gene expression is a fundamental question of molecular biology. We seek to understand this role using a stochastic dynamical model which simulates transcription factor regulatory activity as mediated by epigenetic modification. Our model uses epigenetic data and a gene regulatory network to accurately predict gene expression and explain its predictions through a quantification of regulatory activity. In this way, our method provides insights into the differential regulation of gene expression due to epigenetic modification.

Phage Therapy

The rise of antibiotic resistant bacterial strains has prompted renewed interest in the use of bacteriophages, viruses that infect bacteria, for the treatment of infections. However, the complicated dynamics of phage-bacteria-host interactions makes designing dosage schedules difficult. We seek to use mathematical modeling to understand these dynamics and design optimal dosing strategies for patients with antibiotic resistant infections.

Past Projects

My past work includes projects related to chemical reaction network theory, which is the study of the mathematics of dynamical reaction networks. This work included an investigation of persistence and permanence in reaction networks, as well as work describing equivalence between reaction networks.

I have also published on data collection during an epidemic. In that work, we described a method for assessing confidence of conclusions drawn from biased sampling of the population during an epidemic such as the COVID-19 epidemic of 2020.